Exact Fan-Beam Reconstruction With Arbitrary Object Translations and Truncated Projections

This article proposes a new method for reconstructing two-dimensional (2D) computed tomography (CT) images from truncated and motion contaminated sinograms. The type of motion considered here is a sequence of rigid translations which are assumed to be known. The algorithm first identifies the sufficiency of angular coverage in each 2D point of the CT image to calculate the Hilbert transform from the local “virtual” trajectory which accounts for the motion and the truncation. By taking advantage of data redundancy in the full circular scan, our method expands the reconstructible region beyond the one obtained with chord-based methods. The proposed direct reconstruction algorithm is based on the Differentiated Back-Projection with Hilbert filtering (DBP-H). The motion is taken into account during backprojection which is the first step of our direct reconstruction, before taking the derivatives and inverting the finite Hilbert transform. The algorithm has been tested in a proof-of-concept study on Shepp-Logan phantom simulations with several motion cases and detector sizes.